Is it possible to train deep learning agent to pass a multiple-choice exam?
There are programs that do this today, for some values of "curriculum" and "exam".  It does not even require deep learning; a simpler information retrieval algorithm and some rules for composition work and achieve high scores on machine graded essays.

For human graders, there is research on automatically generating essay-length text responses to queries in a certain domain.

Both linked applications are rule-based rather than based in deep-learning.  I'd guess that a deep-learning approach would be much less efficient (in computer resources) in producing comparable results.